Asymptotically minimax estimation of order-constrained parameters and eigenfunctions of the laplacian on the ball
Adam Korányi; K. Brenda MacGibbon
Annales de l'I.H.P. Probabilités et statistiques (2002)
- Volume: 38, Issue: 2, page 193-206
- ISSN: 0246-0203
Access Full Article
topHow to cite
topKorányi, Adam, and MacGibbon, K. Brenda. "Asymptotically minimax estimation of order-constrained parameters and eigenfunctions of the laplacian on the ball." Annales de l'I.H.P. Probabilités et statistiques 38.2 (2002): 193-206. <http://eudml.org/doc/77713>.
@article{Korányi2002,
author = {Korányi, Adam, MacGibbon, K. Brenda},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {least favorable prior distribution; reflection groups; boundary value problems; asymptotic minimax risk},
language = {eng},
number = {2},
pages = {193-206},
publisher = {Elsevier},
title = {Asymptotically minimax estimation of order-constrained parameters and eigenfunctions of the laplacian on the ball},
url = {http://eudml.org/doc/77713},
volume = {38},
year = {2002},
}
TY - JOUR
AU - Korányi, Adam
AU - MacGibbon, K. Brenda
TI - Asymptotically minimax estimation of order-constrained parameters and eigenfunctions of the laplacian on the ball
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2002
PB - Elsevier
VL - 38
IS - 2
SP - 193
EP - 206
LA - eng
KW - least favorable prior distribution; reflection groups; boundary value problems; asymptotic minimax risk
UR - http://eudml.org/doc/77713
ER -
References
top- [1] P. Berard, Spectres et groupes cristallographiques I: Domaines euclidiens, Inventiones Mathematicae58 (1980) 179-199. Zbl0434.35068MR570879
- [2] P. Berard, G. Besson, Spectres et groupes cristallographiques II: Domaines spheriques, Annales de l'Institut Fourier30 (1980) 237-248. Zbl0426.35073MR597025
- [3] J.O. Berger, Statistical Decision Theory and Bayesian Analysis, Springer-Verlag, New York, 1985. Zbl0572.62008MR804611
- [4] P.E. Berkin, B.Ya. Levit, Second-order asymptotically minimax estimates for the mean of a normal population, Problemy Peredachi Informatsii16 (3) (1980) 60-79, Translation: Problems of Information Transmission (1981) 212–229. Zbl0466.62033
- [5] P.J. Bickel, Minimax estimation of the mean of a normal distribution when the parameter space is restricted, Ann. Statist.9 (1981) 1301-1309. Zbl0484.62013MR630112
- [6] N. Bourbaki, Éléments de mathématique, Fascicule XXXIV, Groupes et algèbres de Lie, Chapitres IV, V et VI, Hermann, Paris, 1969.
- [7] L.D. Brown, Statistical Decision Theory, Mimeographed Notes, Cornell University, Ithaca, NY, 1979.
- [8] L.D. Brown, L. Gajek, Information inequalities for the Bayes risk, Ann. Statist.18 (1990) 1578-1594. Zbl0722.62003MR1074424
- [9] G. Casella, W. Strawderman, Estimating a bounded normal mean, Ann. Statist.9 (1981) 868-876. Zbl0474.62010MR619290
- [10] D.L. Donoho, R.C. Liu, B. MacGibbon, Minimax risk over hyperrectangles and implications, Ann. Statist.18 (1990) 1416-1437. Zbl0705.62018MR1062717
- [11] A. Erdélyi, The Bateman Manuscript Project, Higher Transcendental Functions (3 volumes), McGraw-Hill, New York, 1953–1955, (Erdélyi A. (Ed.)).
- [12] T.S. Ferguson, Mathematical Statistics, A Decision Theoretic Approach, Academic, New York, 1967. Zbl0153.47602MR215390
- [13] G.B. Folland, Introduction to Partial Differential Equations, Princeton University Press, 1995. Zbl0841.35001MR1357411
- [14] D. Gilbarg, N.S. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer-Verlag, Berlin, 1983. Zbl0562.35001MR737190
- [15] G. Harder, A Gauss–Bonnet formula for discrete arithmetically defined groups, Ann. Sci. Ec. Norm. Super.4 (1971) 409-445. Zbl0232.20088
- [16] I.M. Johnstone, K.B. MacGibbon, Minimax estimation of a constrained Poisson vector, Ann. Statist.20 (1992) 807-831. Zbl0761.62006MR1165594
- [17] I.M. Johnstone, K.B. MacGibbon, Asymptotically minimax estimation of a constrained Poisson vector via polydisc transforms, Annales de l'Institut Henri Poincaré, Probabilité et Statistiques29 (1993) 289-319. Zbl0779.62022MR1227421
- [18] P.J. Kempthorne, Numerical specification of discrete least favorable prior distributions, SIAM J. Sci. Statist. Comput.8 (1987) 171-184. Zbl0618.65147MR879409
- [19] B.Ya. Levit, On asymptotic minimax estimates of the second order, Theor. Probab. Appl.25 (1980) 552-568, (Translation). Zbl0494.62035
- [20] B.Ya. Levit, Minimax estimation and positive solutions of elliptic equations, Theor. Probab. Appl.27 (1982) 563-586, (Translation). Zbl0518.62031MR673924
- [21] B.Ya. Levit, Second order asymptotic optimality and positive solutions of Schrödinger's equation, Theor. Probab. Appl.30 (1985) 333-363, (Translation). Zbl0608.62035MR792622
- [22] B.Ya. Levit, Evaluation of the minimax risk, in: Proc. Fourth International Vilnius Conf. Prob. Theory Math. Stat., Vilnius, Vol. 4, 1985, pp. 181-183.
- [23] B.Ya. Levit, On second order admissibility in simultaneous estimation, in: Prohorov Yu.A., Sazonov V.V. (Eds.), Proc. 1st. World Congress Bernoulli Soc. Tashkent, USSR, VNU Sc. Press, Ultrecht, 1986. Zbl0686.62017MR1092458
- [24] P.G. MacDonald, The volume of a compact Lie Group, Inventiones Mathematicae56 (1980) 93-95. Zbl0426.22009MR558859
- [25] T. Robertson, F.T. Wright, R.L. Dykstra, Order Restricted Statistical Inference, Wiley, New York, 1988. Zbl0645.62028MR961262
- [26] D.A. Schoenfeld, Confidence bounds for normal means under order restrictions, with applications to dose-response curves, toxicology experiments, and low-dose extrapolation, J. Amer. Statist. Assoc.81 (1986) 186-195. Zbl0587.62194
- [27] H. Urakawa, Bounded domains which are isospectral but not congruent, Ann. Sci. Ec. Norm. Super.IV (15) (1982) 441-456. Zbl0505.58036MR690649
- [28] H. Urakawa, Reflection groups and the eigenvalue problems of vibrating membranes with mixed boundary conditions, Tohoku Math. J.II (36) (1984) 175-183. Zbl0552.35014MR742592
- [29] A. Wald, Statistical Decision Functions, Wiley, New York, 1950. Zbl0040.36402MR36976
- [30] G. Watson, A Treatise on the Theory of Bessel Functions, Cambridge University Press, Cambridge, 1962. MR1349110JFM50.0264.01
- [31] E. Zinzius, Minimaxschatzer für den Mittelwert υ einer normalverteilten Zufallgröße mit bekannter Varianz bei vorgegebener oberer und unterer Schranke für υ, Math. Operationsforsch. Statist. Ser. Statist.12 (1981) 551-557. Zbl0514.62013
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.